A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method

In the present paper, a new analytical technique based on the rational harmonic balance method (RHBM) has been introduced to determine approximate periodic solutions for the nonlinear non-smooth oscillator. A frequency–amplitude relationship has also been obtained by a novel analytical way. The stan...

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Main Authors:	Hosen, Md. Alal, Chowdhury, Md. Sazzad Hossien, Ali, Mohammad Yeakub, Ismail, Ahmad Faris
Format:	Conference or Workshop Item
Language:	English
Published:	Springer Nature Singapore Pte Ltd. 2018
Subjects:	T Technology (General) T55.4 Industrial engineering.Management engineering. TJ Mechanical engineering and machinery TS Manufactures
Online Access:	http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/8/64006%20A%20New%20Analytical%20Technique%20for%20Solving%20Nonlinear.pdf

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recordtype	eprints
spelling	iium-640062018-06-07T01:12:43Z http://irep.iium.edu.my/64006/ A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris T Technology (General) T55.4 Industrial engineering.Management engineering. TJ Mechanical engineering and machinery TS Manufactures In the present paper, a new analytical technique based on the rational harmonic balance method (RHBM) has been introduced to determine approximate periodic solutions for the nonlinear non-smooth oscillator. A frequency–amplitude relationship has also been obtained by a novel analytical way. The standard rational harmonic balance method (SRHBM) cannot be used directly; it is possible if we rewrite the nonlinear differential equations (NDEs). To overcome this previously stated issue, we offered a modified rational harmonic balance method (MRHBM). It is noticed that a MRHBM works very well for the whole range of initial amplitudes and the excellent agreement of the approximate frequencies as well as the corresponding periodic solutions with its exact ones. The method is basically illustrated by the nonlinear non-smooth oscillators, but it is additionally useful for other nonlinear oscillatory problems with mixed parity arising in recent development of nonlinear sciences and engineering. Springer Nature Singapore Pte Ltd. 2018 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/64006/8/64006%20A%20New%20Analytical%20Technique%20for%20Solving%20Nonlinear.pdf Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2018) A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method. In: Second International Conference on the Future of ASEAN (ICoFA) 2017, 15-16 August 2017, Kangar, Perlis. https://link.springer.com/chapter/10.1007/978-981-10-8471-3_45 10.1007/978-981-10-8471-3_45
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	T Technology (General) T55.4 Industrial engineering.Management engineering. TJ Mechanical engineering and machinery TS Manufactures
spellingShingle	T Technology (General) T55.4 Industrial engineering.Management engineering. TJ Mechanical engineering and machinery TS Manufactures Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method
description	In the present paper, a new analytical technique based on the rational harmonic balance method (RHBM) has been introduced to determine approximate periodic solutions for the nonlinear non-smooth oscillator. A frequency–amplitude relationship has also been obtained by a novel analytical way. The standard rational harmonic balance method (SRHBM) cannot be used directly; it is possible if we rewrite the nonlinear differential equations (NDEs). To overcome this previously stated issue, we offered a modified rational harmonic balance method (MRHBM). It is noticed that a MRHBM works very well for the whole range of initial amplitudes and the excellent agreement of the approximate frequencies as well as the corresponding periodic solutions with its exact ones. The method is basically illustrated by the nonlinear non-smooth oscillators, but it is additionally useful for other nonlinear oscillatory problems with mixed parity arising in recent development of nonlinear sciences and engineering.
format	Conference or Workshop Item
author	Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris
author_facet	Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris
author_sort	Hosen, Md. Alal
title	A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method
title_short	A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method
title_full	A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method
title_fullStr	A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method
title_full_unstemmed	A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method
title_sort	new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method
publisher	Springer Nature Singapore Pte Ltd.
publishDate	2018
url	http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/8/64006%20A%20New%20Analytical%20Technique%20for%20Solving%20Nonlinear.pdf
first_indexed	2023-09-18T21:30:46Z
last_indexed	2023-09-18T21:30:46Z
_version_	1777412495359606784

A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method

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